Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2

Percentage Accurate: 100.0% → 100.0%

Time: 2.0s

Alternatives: 4

Speedup: N/A×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ e^{\left(x \cdot y\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))

C

double code(double x, double y) {
	return exp(((x * y) * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(((x * y) * y))
end function

Java

public static double code(double x, double y) {
	return Math.exp(((x * y) * y));
}

Python

def code(x, y):
	return math.exp(((x * y) * y))

Julia

function code(x, y)
	return exp(Float64(Float64(x * y) * y))
end

MATLAB

function tmp = code(x, y)
	tmp = exp(((x * y) * y));
end

Wolfram

code[x_, y_] := N[Exp[N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{\left(x \cdot y\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))

C

double code(double x, double y) {
	return exp(((x * y) * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(((x * y) * y))
end function

Java

public static double code(double x, double y) {
	return Math.exp(((x * y) * y));
}

Python

def code(x, y):
	return math.exp(((x * y) * y))

Julia

function code(x, y)
	return exp(Float64(Float64(x * y) * y))
end

MATLAB

function tmp = code(x, y)
	tmp = exp(((x * y) * y));
end

Wolfram

code[x_, y_] := N[Exp[N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{x \cdot \left(y \cdot y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (exp (* x (* y y))))

C

double code(double x, double y) {
	return exp((x * (y * y)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp((x * (y * y)))
end function

Java

public static double code(double x, double y) {
	return Math.exp((x * (y * y)));
}

Python

def code(x, y):
	return math.exp((x * (y * y)))

Julia

function code(x, y)
	return exp(Float64(x * Float64(y * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = exp((x * (y * y)));
end

Wolfram

code[x_, y_] := N[Exp[N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]
2. Step-by-step derivation

   1. associate-*l* 100.0%

      \[\leadsto e^{\color{blue}{x \cdot \left(y \cdot y\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{e^{x \cdot \left(y \cdot y\right)}} \]

4. Final simplification 100.0%

   \[\leadsto e^{x \cdot \left(y \cdot y\right)} \]

Alternative 2: 56.9% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{+148}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2.7e+148) 1.0 (* x (* y y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.7e+148) {
		tmp = 1.0;
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2.7d+148) then
        tmp = 1.0d0
    else
        tmp = x * (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.7e+148) {
		tmp = 1.0;
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.7e+148:
		tmp = 1.0
	else:
		tmp = x * (y * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.7e+148)
		tmp = 1.0;
	else
		tmp = Float64(x * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.7e+148)
		tmp = 1.0;
	else
		tmp = x * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.7e+148], 1.0, N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.70000000000000019e148

   1. Initial program 99.9%

      \[e^{\left(x \cdot y\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 100.0%

         \[\leadsto e^{\color{blue}{x \cdot \left(y \cdot y\right)}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{e^{x \cdot \left(y \cdot y\right)}} \]

   4. Taylor expanded in x around 0 63.3%

      \[\leadsto \color{blue}{1} \]

   if 2.70000000000000019e148 < y

   1. Initial program 100.0%

      \[e^{\left(x \cdot y\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 100.0%

         \[\leadsto e^{\color{blue}{x \cdot \left(y \cdot y\right)}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{e^{x \cdot \left(y \cdot y\right)}} \]

   4. Taylor expanded in x around 0 44.8%

      \[\leadsto \color{blue}{1 + {y}^{2} \cdot x} \]
   5. Step-by-step derivation

      1. unpow2 44.8%

         \[\leadsto 1 + \color{blue}{\left(y \cdot y\right)} \cdot x \]

      2. *-commutative 44.8%

         \[\leadsto 1 + \color{blue}{x \cdot \left(y \cdot y\right)} \]

   6. Simplified 44.8%

      \[\leadsto \color{blue}{1 + x \cdot \left(y \cdot y\right)} \]

   7. Taylor expanded in x around inf 44.8%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} \]
   8. Step-by-step derivation

      1. unpow2 44.8%

         \[\leadsto \color{blue}{\left(y \cdot y\right)} \cdot x \]

      2. *-commutative 44.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot y\right)} \]

   9. Simplified 44.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{+148}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 3: 66.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y \cdot y\right) + 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (* x (* y y)) 1.0))

C

double code(double x, double y) {
	return (x * (y * y)) + 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * (y * y)) + 1.0d0
end function

Java

public static double code(double x, double y) {
	return (x * (y * y)) + 1.0;
}

Python

def code(x, y):
	return (x * (y * y)) + 1.0

Julia

function code(x, y)
	return Float64(Float64(x * Float64(y * y)) + 1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * (y * y)) + 1.0;
end

Wolfram

code[x_, y_] := N[(N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]
2. Step-by-step derivation

   1. associate-*l* 100.0%

      \[\leadsto e^{\color{blue}{x \cdot \left(y \cdot y\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{e^{x \cdot \left(y \cdot y\right)}} \]

4. Taylor expanded in x around 0 64.7%

   \[\leadsto \color{blue}{1 + {y}^{2} \cdot x} \]
5. Step-by-step derivation

   1. unpow2 64.7%

      \[\leadsto 1 + \color{blue}{\left(y \cdot y\right)} \cdot x \]

   2. *-commutative 64.7%

      \[\leadsto 1 + \color{blue}{x \cdot \left(y \cdot y\right)} \]

6. Simplified 64.7%

   \[\leadsto \color{blue}{1 + x \cdot \left(y \cdot y\right)} \]

7. Final simplification 64.7%

   \[\leadsto x \cdot \left(y \cdot y\right) + 1 \]

Alternative 4: 50.7% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]
2. Step-by-step derivation

   1. associate-*l* 100.0%

      \[\leadsto e^{\color{blue}{x \cdot \left(y \cdot y\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{e^{x \cdot \left(y \cdot y\right)}} \]

4. Taylor expanded in x around 0 53.7%

   \[\leadsto \color{blue}{1} \]

5. Final simplification 53.7%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))